Complete Elgot Monads and Coalgebraic Resumptions
Author(s): Goncharov S, Milius S, Rauch C
Editor(s): Lars Birkedal
Publisher: Electronic Notes in Theoretical Computer Science
Publication year: 2016
Pages range: 147--168
Event: MFPS XXXII
Event location: Carnegie Mellon University, Pittsburgh
Start date of the event: 23/05/2016
End date of the event: 26/05/2016
Monads are used to abstractly model a wide range of computational effects such as nondeterminism, statefulness, and exceptions. Complete Elgot monads are monads that are equipped with a (uniform) iteration operator satisfying a set of natural axioms, which allows to model iterative computations just as abstractly. It has been shown recently that extending complete Elgot monads with free effects (e.g. operations of sending/receiving messages over channels) canonically leads to generalized coalgebraic resumption monads, which were previously used as semantic domains for non-wellfounded guarded processes. In this paper, we continue the study of complete Elgot monads and their relationship with generalized coalgebraic resumption monads. We give a characterization of the Eilenberg-Moore algebras of the latter. In fact, we work more generally with Uustalu's parametrized monads; we introduce complete Elgot algebras for a parametrized monad and we prove that they form an Eilenberg-Moore category. This is further used for establishing a characterization of complete Elgot monads as those monads whose algebras are coherently equipped with the structure of complete Elgot algebras for the parametrized monads obtained from generalized coalgebraic resumption monads.
FAU Authors / FAU Editors How to cite
APA: Goncharov, S., Milius, S., & Rauch, C. (2016). Complete Elgot Monads and Coalgebraic Resumptions. In Lars Birkedal (Eds.), (pp. 147--168). Electronic Notes in Theoretical Computer Science.
MLA: Goncharov, Sergey, Stefan Milius, and Christoph Rauch. "Complete Elgot Monads and Coalgebraic Resumptions." Proceedings of the MFPS XXXII, Carnegie Mellon University, Pittsburgh Ed. Lars Birkedal, Electronic Notes in Theoretical Computer Science, 2016. 147--168.